Rate gyroscopes are sensors that measure rotation rate. Rate gyroscopes have uses in many commercial, military, and scientific applications including, but not limited to, inertial navigation, vehicular skid control, and platform stabilization.
A vibratory rate gyroscope is a sensor that responds to rotation rate by generating and measuring Coriolis acceleration. Coriolis acceleration is generated by any object (such as a proof-mass) that has a non-zero velocity relative to a rotating reference frame. In vibratory rate gyroscopes, one or more proof-masses are suspended by springs and made to oscillate. This driven-mode oscillation supplies the velocity necessary to generate Coriolis acceleration under an input rotation. The component of Coriolis acceleration along an axis, y, is given by: EQU .alpha..sub.y =2.OMEGA..sub.z (t)D.sub.x.omega..sub.x cos(.omega..sub.x t) (Equation 1)
where x, y, and z are three mutually orthogonal axes, .OMEGA..sub.z is the input rotation rate about the z-axis, .omega..sub.x is the driven mode oscillation frequency, D.sub.x is the displacement amplitude of the oscillation in the driven mode, and ay is the resulting Coriolis acceleration. If the amplitude, D.sub.x, and driven-mode frequency, .omega..sub.x, are known, measurement of the Coriolis acceleration may be used to estimate the rotation rate of the sensor.
As shown in Equation 1, the Coriolis acceleration is directly proportional to the rotation-rate input, the magnitude of the drive-mode oscillation, and the frequency of the drive-mode oscillation. Changes in driven-mode oscillation frequency that occur over time or with temperature cause first-order errors in the sensor output, as do variations in the amplitude of this oscillation. For a high-stability gyroscope, the oscillation amplitude and frequency must both be precisely controlled.
Operation of a gyroscope in a vacuum is often desirable to minimize both noise and resistance to oscillation. Note that in a vacuum, the lack of mechanical damping may cause large variations in the magnitude of the driven-mode oscillation in response to mechanical shocks or external accelerations. In addition, the high mechanical quality-factor of vibrational modes in vacuum result in output errors that last long after the source of disturbance has been removed. Thus, it is clear that methods that do not actively control the amplitude of the drive-mode oscillation will achieve poor performance in the face of external disturbance.
Oscillation of the gyroscope may be both forced and detected using variable air-gap capacitors. Electrostatic forces result between charged capacitor plates. The magnitude and direction of the force is given by the gradient of the potential energy function for the capacitor as shown below. ##EQU1##
To generate a appropriate oscillation in a gyroscope, a force along a single axis, the X-axis for example, is required. Equation 2 implies that any capacitor that varies with displacement along the X-axis will generate an appropriate force. An implementation of a pair of such capacitors is shown in FIG. 1. This capacitor configuration has a number of advantages including ample room for large displacements along the X-axis without collisions between comb fingers. By applying differential voltages with a common mode bias V.sub.DC across electrically conductive comb fingers 102, 103a and 102,103b, a force that is independent of X-axis displacement and linear with control voltage, v.sub.x is created: ##EQU2##
where C.sub.0 and X.sub.0 are the capacitance and X-axis overlap of the air-gap capacitors at zero displacement respectively. An alternative method of applying forces chooses V.sub.1, V.sub.2 such that: EQU V.sub.1 =V.sub.DC -v.sub.x EQU V.sub.2 =-V.sub.DC -v.sub.x (Equation 4)
Note that in both of these cases the magnitude of the force is proportional to the control voltage, v.sub.x, and the DC bias voltage, V.sub.DC. This permits the magnitude of the force to be linearly controlled by varying either v.sub.x or V.sub.DC while maintaining the other voltage constant.
A second configuration achieving the desired goal of applying force along a single axis is shown in FIG. 2. This method uses sets of interdigitated comb fingers 103c, 102b, 103d to apply forces in the positive and negative directions. The net forces on the proof-mass at zero displacement are given by: ##EQU3##
where V.sub.1, V.sub.2 are as defined in either Equation 3 or 4. Note that while the forces are linear with applied voltage v.sub.X or V.sub.DC, the forces are highly dependent on the proof-mass displacement, resulting in poor performance over even small motions. This problem may be surmounted by controlling charges instead of voltages on the two capacitors. Given bias and control charges Q.sub.DC and q.sub.x, the resulting force may be found to equal: ##EQU4##
where .epsilon..sub.0 and A are the permittivity of free space and overlap area of the interdigitated comb fingers respectively. The above equations show that the nonlinearity with displacement is thus avoided.
Sensing of driven mode deflections may be attained by measuring capacitance. There are two approaches commonly taken in a capacitive sensing. In the first approach, illustrated in FIG. 3(a) and FIG. 3(b), a changing voltage is applied to two nominally equal-sized capacitors. Any imbalance between these capacitors results in charge that is measured by a sense interface 104a,b. The second method, illustrated in FIG. 3(c) and FIG. 3(d), uses a constant DC bias voltage applied across the capacitors. Any change in the capacitance values results in current flow that is detected by a sense interface 104c,d. Both methods are illustrated in FIG. 3 with differential (FIG. 3(a) and (c)) and single-ended (FIG. 3(b) and (d)) sense interfaces. The capacitors, which vary with X-axis or driven-mode displacements, are similar to those shown in FIG. 1 or FIG. 2.
The sense interfaces or sense amplifiers discussed above usually take the form of either a transresistance amplifier, a voltage buffer, or a charge integrator. Simplified, single-ended configurations of these topologies are shown in FIG. 4(a), (b), and (c) respectively. The transresistance amplifier converts input current to an output voltage whereas the voltage buffer and integrator convert input charge to an output voltage when connected to a capacitor bridge circuit.
The trans resistance amplifier may be used with a DC sense voltage to yield a measure of the proof-mass velocity. Velocity is measured because the current generated by deflections in the capacitor bridge circuit is a function of velocity. The voltage buffer and charge integrator measure the deflection of the proof-mass in both the pulsed and DC bias configurations.
Provided with a controllable force applied to a structure and a measure of the structure's deflection, the structure may be driven into oscillation using feedback. Desired oscillation is achieved by measuring the structure's displacement or velocity then determining the magnitude and/or direction of the force to apply to the structure. The measurement of the structure's displacement and the force applied may be electrostatic as described above. The measurement of the structure's displacement may be fed back as a force either directly or filtered depending on the nature of the oscillation loop.